Training neural network for good taste in art
This question reminds me of a project I saw that used Deep Learning to rate selfies on twitter. But a quick google search shows that there are plenty of projects that are much closer to what you are interested in:

Rating Image Aesthetics using Deep Learning

Predicting Image Aesthetics with Deep Learning

Deep Understanding of Image Aesthetics (with data and model linked)

Understanding Aesthetics with Deep Learning

and probably dozens more. 

Of course if you are interested in predicting subjective pleasantness the above is only a beginning. In that case you may also take a look at recommender systems.